I take it you want to reuse some of the parts in the older computer in a new build? There are a few internal parts that can work, including some hard drives, optical drives and sometimes, the case. Regarding the case, it really depends on how old it is, and what form factor it uses.
Modern computers use ATX cases. Very, very old cases used the AT form which is not compatible with modern computers. And there was the briefly used BTX case, which was mostly found in a few OEM companies like Dell.
Another problem with older cases is that they often used small, noisy fans. Modern cases will use 120mm and larger fans for cooling.
I wouldn't recommend an old psu in a modern machine. But it really depends on how old this one is and its rating.
So when you come down to it, you can't really salvage much from an older machine, say 5yrs old or so. The psu requirements are different, the memory is different, the modern motherboard may not have an IDE connection for older hard drives and older optical drives.
So, we'd have to know all the specifics of your computer that you want to upgrade. And I mean, kill us with details. The more we know, the better we will be able to advise you.
This discussion would probably be better off in the General Hardware forum, so I'm going to move it in there and leave a redirect in the Newbies for you.